Journal
JOURNAL OF MATHEMATICAL PSYCHOLOGY
Volume 53, Issue 6, Pages 577-585Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jmp.2009.08.003
Keywords
Combinatorial data analysis; Blockmodeling; Integer programming
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Funding
- NIAAA NIH HHS [K25 AA017456, K25 AA017456-02] Funding Source: Medline
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Establishing blockmodels for one- and two-mode binary network matrices has typically been accomplished using multiple restarts of heuristic algorithms that minimize functions of inconsistency with an ideal block structure. Although these algorithms likely yield exceptional performance, they are not assured to provide blockmodels that optimize the functional indices. In this paper, we present integer programming models that, for a prespecified image matrix, can produce guaranteed optimal solutions for matrices of nontrivial size. Accordingly, analysts performing a confirmatory analysis of a prespecified blockmodel structure can apply our models directly to obtain an optimal solution. In exploratory cases where a blockmodel structure is not prespecified, we recommend a two-stage procedure, where a heuristic method is first used to identify an image matrix and the integer program is subsequently formulated and solved to identify the optimal solution for that image matrix. Although best suited for ideal block structures associated with structural equivalence, the integer programming models have the flexibility to accommodate functional indices pertaining to regular equivalence. Computational results are reported for a variety of one- and two-mode matrices from the blockmodeling literature. (C) 2009 Elsevier Inc. All rights reserved.
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